Problem $1.$ Financing a home. You borrow $$200,000$ to finance the purchase

of a new home with a $30-$year, fully$-$amortizing, fixed$-$rate mortgage with an APR

of $6\%($compounded monthly$).$

$($a$)$ What are your payments each month?

$($b$)$ What is the remaining principal balance on the loan after $3$ years $($i$.$e$.,$ just after

making your $36$th payment$)?$